Since 2013, Wright has appeared in the Netflix political drama web television series House of Cards in the role of Claire Underwood, the ruthless wife of political mastermind Frank Underwood. On January 12, 2014, she won a Golden Globe for the role, becoming the first actress to win the award for an online-only web television series;[7] she was nominated for the same award the following year. She also received nominations for the Primetime Emmy Award in 2013 and 2014 for the same role. Following Season 4 in 2016, Wright stated that she felt Claire Underwood was the equal of Frank Underwood and demanded equal pay for her performance as her co-star Kevin Spacey; Netflix acquiesced.[8] In 2017, for her performance in the fifth season, Wright was nominated for her fifth consecutive Primetime Emmy nomination for Outstanding Lead Actress – Drama. For the years 2014, 2016, and 2017, Wright received Best Actress in a Drama Series nominations for the Critics' Choice Television Awards, with her being the only nomination for the show in December 2017. In October 2017, Wright was set as the show's new lead, following sexual misconduct allegations against Spacey, which resulted in him being fired from the sixth and final season.

After breaking up and getting back together,[13] Wright and Penn married in 1996, and she changed her name to Robin Wright Penn.[14] Their on-and-off relationship seemingly ended in divorce plans, announced in December 2007,[14] but the divorce petition was withdrawn four months later at the couple's request.[15] In February 2009, Wright and Penn attended the 81st Academy Awards together, at which Penn won Best Actor. Penn filed for legal separation in April 2009,[16] but withdrew the petition in May.[17] On August 12, 2009, Wright filed for divorce declaring she had no plans to reconcile.[18][19] At that time she dropped "Penn" from her professional name.[20] The divorce was finalized on July 22, 2010.[21]

In February 2012, Wright began dating actor Ben Foster,[22] and their engagement was announced in January 2014.[23][24] The couple called off their engagement in November 2014,[25] but reunited in January 2015.[26] On August 29, 2015, they announced they were ending their second engagement.[27]

In 2014, Wright co-partnered with two California based companies; Pour Les Femmes[29] and The SunnyLion.[30] The SunnyLion donates a portion of its profits to the Raise Hope For Congo movement.

Wright is an activist for human rights in the Democratic Republic of the Congo. She is the narrator and executive producer of the documentary When Elephants Fight[31] which highlights how multinational mining corporations and politicians in the Democratic Republic of Congo threaten human rights, and perpetuate conflict in the region.[32] Wright is a supporter of Stand With Congo, the human rights campaign behind the film.[33] In 2016, she spoke publicly in support of the campaign at a film screening at the TriBeCa Film Institute in New York City,[34] in media interviews,[35][36][37][38] with journalists,[39][40][41] and across her social media accounts.[42][43][44]